Ball, J. M. (1997) Continuity Properties and Global Attractors of Generalized Semiflows and the Navier-Stokes Equations. Journal of Nonlinear Science, 7 (5). pp. 475-502. ISSN 0938-8974 (Paper) 1432-1467 (Online)
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Abstract
A class of semiflows having possibly nonunique solutions is defined. The measurability and continuity properties of such generalized semiflows are studied. It is shown that a generalized semiflow has a global attractor if and only if it is pointwise dissipative and asymptotically compact. The structure of the global attractor in the presence of a Lyapunov function, and its connectedness and stability properties are studied. In particular, examples are given in which the global attractor is a single point but is not Lyapunov stable.
The existence of a global attractor for the 3D incompressible Navier-Stokes equations is established under the (unproved) hypothesis that all weak solutions are continuous from to
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| Item Type: | Article |
|---|---|
| Additional Information: | There is a one-page erratum to this paper. http://www.springerlink.com/openurl.asp?genre=article&eissn=1432-1467&volume=8&issue=2&spage=233 |
| Subjects: | O - Z > Partial differential equations D - G > Dynamical systems and ergodic theory D - G > Fluid mechanics |
| Research Groups: | Oxford Centre for Nonlinear PDE |
| ID Code: | 197 |
| Deposited By: | John Ball |
| Deposited On: | 30 Aug 2005 |
| Last Modified: | 20 Jul 2009 14:19 |
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